Find the volume of a right circular cone that has a height of 15.8ft and a base with a diameter of 11.3ft. Round your answer to the nearest tenth of a cubic foot. Answer: ft^(3)

Find Radius: To find the volume of a cone, we use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. First, we need to find the radius of the base. The diameter is given as 11.3 feet, so the radius is half of that. Radius (r) = Diameter / 2 = 11.3 ft / 2Calculate Radius: Now we calculate the radius: r = 11.3 ft / 2 = 5.65 ftPlug into Volume Formula: Next, we plug the radius and the height into the volume formula: V = (1/3)π(5.65 ft)^2(15.8 ft)Calculate Volume: We calculate the volume: V = (1/3)π(5.65 ft)^2(15.8 ft) = (1/3)π(31.9225 ft^2)(15.8 ft)Perform Multiplication: Now we perform the multiplication: V = (1/3)π(31.9225 ft^2)(15.8 ft) = (1/3)π(504.675 ft^3)Find Final Volume: Finally, we multiply by π and divide by 3 to find the volume: V = (1/3)π(504.675 ft^3) ≈ (1/3)(3.14159)(504.675 ft^3) ≈ 530.093 ft^3Round the Answer: We round the answer to the nearest tenth of a cubic foot: V ≈ 530.1 ft^3

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the volume of a right circular cone that has a height of
15.8ft and a base with a diameter of
11.3ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
ft^(3)

Find the volume of a right circular cone that has a height of $15.8 \mathrm{ft}$ and a base with a diameter of $11.3 \mathrm{ft}$ . Round your answer to the nearest tenth of a cubic foot. $\newline$ Answer: $\mathrm{ft}^{3}$

View step-by-step help

Home

Math Problems

Grade 7

Convert between customary and metric systems

Full solution

Q. Find the volume of a right circular cone that has a height of

15.8 \mathrm{ft}

and a base with a diameter of

11.3 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

Answer:

\mathrm{ft}^{3}

Find Radius: To find the volume of a cone, we use the formula $V = \frac{1}{3}\pi r^2 h$ , where $r$ is the radius of the base and $h$ is the height of the cone. First, we need to find the radius of the base. The diameter is given as $11.3$ feet, so the radius is half of that. $\newline$ Radius $r$ = Diameter / $2$ = $11.3$ ft / $2$
Calculate Radius: Now we calculate the radius: $r = \frac{11.3 \, \text{ft}}{2} = 5.65 \, \text{ft}$
Plug into Volume Formula: Next, we plug the radius and the height into the volume formula: $\newline$ $V = \frac{1}{3}\pi(5.65 \text{ ft})^2(15.8 \text{ ft})$
Calculate Volume: We calculate the volume: $V = \frac{1}{3}\pi(5.65 \text{ ft})^2(15.8 \text{ ft}) = \frac{1}{3}\pi(31.9225 \text{ ft}^2)(15.8 \text{ ft})$
Perform Multiplication: Now we perform the multiplication: $V = \frac{1}{3}\pi(31.9225 \text{ ft}^2)(15.8 \text{ ft}) = \frac{1}{3}\pi(504.675 \text{ ft}^3)$
Find Final Volume: Finally, we multiply by $\pi$ and divide by $3$ to find the volume: $V = \frac{1}{3}\pi(504.675 \text{ ft}^3) \approx \frac{1}{3}(3.14159)(504.675 \text{ ft}^3) \approx 530.093 \text{ ft}^3$
Round the Answer: We round the answer to the nearest tenth of a cubic foot: $V \approx 530.1 \, \text{ft}^3$